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Question

(b) Consider the MAP estimate,

θ^MAP=argmaxθ p(θ∣D).(3.47)\hat{\theta}_{MAP} = \underset{\theta}{\text{argmax}} \, p(\theta|\mathcal{D}). \tag{3.47}

How does it differ from the least squares estimate and the weighted-least squares estimate? What is the role of the terms that were not present before? Is there any advantage in setting them to anything other than zero?